TSTP Solution File: GRP530-1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP530-1 : TPTP v3.4.2. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:07:06 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_these_axioms_2,plain,
~ $equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP530-1.tptp',unknown),
[] ).
cnf(150781632,plain,
~ $equal(multiply(multiply(inverse(b2),b2),a2),a2),
inference(rewrite,[status(thm)],[prove_these_axioms_2]),
[] ).
fof(multiply,plain,
! [A,C,B] : $equal(divide(A,divide(divide(C,C),B)),multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP530-1.tptp',unknown),
[] ).
cnf(150752656,plain,
$equal(divide(A,divide(divide(C,C),B)),multiply(A,B)),
inference(rewrite,[status(thm)],[multiply]),
[] ).
cnf(158605960,plain,
~ $equal(divide(multiply(inverse(b2),b2),divide(divide(A,A),a2)),a2),
inference(paramodulation,[status(thm)],[150781632,150752656,theory(equality)]),
[] ).
fof(inverse,plain,
! [B,A] : $equal(divide(divide(B,B),A),inverse(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP530-1.tptp',unknown),
[] ).
cnf(150776968,plain,
$equal(divide(divide(B,B),A),inverse(A)),
inference(rewrite,[status(thm)],[inverse]),
[] ).
cnf(158794800,plain,
~ $equal(divide(multiply(inverse(b2),b2),inverse(a2)),a2),
inference(paramodulation,[status(thm)],[158605960,150776968,theory(equality)]),
[] ).
cnf(158919296,plain,
~ $equal(divide(divide(inverse(b2),divide(divide(A,A),b2)),inverse(a2)),a2),
inference(paramodulation,[status(thm)],[158794800,150752656,theory(equality)]),
[] ).
cnf(159514432,plain,
~ $equal(divide(divide(inverse(b2),inverse(b2)),inverse(a2)),a2),
inference(paramodulation,[status(thm)],[158919296,150776968,theory(equality)]),
[] ).
cnf(159582984,plain,
~ $equal(inverse(inverse(a2)),a2),
inference(paramodulation,[status(thm)],[159514432,150776968,theory(equality)]),
[] ).
cnf(159629784,plain,
~ $equal(divide(divide(A,A),inverse(a2)),a2),
inference(paramodulation,[status(thm)],[159582984,150776968,theory(equality)]),
[] ).
cnf(159691736,plain,
~ $equal(divide(divide(A,A),divide(divide(B,B),a2)),a2),
inference(paramodulation,[status(thm)],[159629784,150776968,theory(equality)]),
[] ).
fof(single_axiom,plain,
! [A,B,C] : $equal(divide(divide(A,divide(B,C)),divide(A,B)),C),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP530-1.tptp',unknown),
[] ).
cnf(150728880,plain,
$equal(divide(divide(A,divide(B,C)),divide(A,B)),C),
inference(rewrite,[status(thm)],[single_axiom]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[159691736,150728880]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_these_axioms_2,plain,(~$equal(multiply(multiply(inverse(b2),b2),a2),a2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP530-1.tptp',unknown),[]).
%
% cnf(150781632,plain,(~$equal(multiply(multiply(inverse(b2),b2),a2),a2)),inference(rewrite,[status(thm)],[prove_these_axioms_2]),[]).
%
% fof(multiply,plain,($equal(divide(A,divide(divide(C,C),B)),multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP530-1.tptp',unknown),[]).
%
% cnf(150752656,plain,($equal(divide(A,divide(divide(C,C),B)),multiply(A,B))),inference(rewrite,[status(thm)],[multiply]),[]).
%
% cnf(158605960,plain,(~$equal(divide(multiply(inverse(b2),b2),divide(divide(A,A),a2)),a2)),inference(paramodulation,[status(thm)],[150781632,150752656,theory(equality)]),[]).
%
% fof(inverse,plain,($equal(divide(divide(B,B),A),inverse(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP530-1.tptp',unknown),[]).
%
% cnf(150776968,plain,($equal(divide(divide(B,B),A),inverse(A))),inference(rewrite,[status(thm)],[inverse]),[]).
%
% cnf(158794800,plain,(~$equal(divide(multiply(inverse(b2),b2),inverse(a2)),a2)),inference(paramodulation,[status(thm)],[158605960,150776968,theory(equality)]),[]).
%
% cnf(158919296,plain,(~$equal(divide(divide(inverse(b2),divide(divide(A,A),b2)),inverse(a2)),a2)),inference(paramodulation,[status(thm)],[158794800,150752656,theory(equality)]),[]).
%
% cnf(159514432,plain,(~$equal(divide(divide(inverse(b2),inverse(b2)),inverse(a2)),a2)),inference(paramodulation,[status(thm)],[158919296,150776968,theory(equality)]),[]).
%
% cnf(159582984,plain,(~$equal(inverse(inverse(a2)),a2)),inference(paramodulation,[status(thm)],[159514432,150776968,theory(equality)]),[]).
%
% cnf(159629784,plain,(~$equal(divide(divide(A,A),inverse(a2)),a2)),inference(paramodulation,[status(thm)],[159582984,150776968,theory(equality)]),[]).
%
% cnf(159691736,plain,(~$equal(divide(divide(A,A),divide(divide(B,B),a2)),a2)),inference(paramodulation,[status(thm)],[159629784,150776968,theory(equality)]),[]).
%
% fof(single_axiom,plain,($equal(divide(divide(A,divide(B,C)),divide(A,B)),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP530-1.tptp',unknown),[]).
%
% cnf(150728880,plain,($equal(divide(divide(A,divide(B,C)),divide(A,B)),C)),inference(rewrite,[status(thm)],[single_axiom]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[159691736,150728880]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------